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  • McCumber relation
    =\exp\!\left( \frac{\hbar \omega_{\rm z}}{k_{\rm B} T}\right)</math> is thermal steady-state ratio of populations; frequency <math>\omega_{\rm z}</math> is called "zero-line" frequency <ref name="comment">
    16 KB (2,521 words) - 15:13, 17 June 2020
  • Factorial
    :<math> F(z+1)=(z+1) F(z) </math> for all complex <math>z</math> except negative integer values.
    27 KB (3,925 words) - 18:26, 30 July 2019
  • C2011mar16.cc
    main(){ int m,n,k; DB x,y,z, X[49],Y[49], Z[49][17]; char c,d, namae[32]; ...6;k++){ fscanf(i,"%lf",&z); if(z==0) z=1.; printf(" %5.3lf",z); Z[n][k]=z;}
    4 KB (678 words) - 14:24, 20 June 2013
  • C2011mar17.cc
    main(){ int m,n,k; DB x,y,z, X[49],Y[49], Z[49][17]; char c,d, namae[32]; ...6;k++){ fscanf(i,"%lf",&z); if(z==0) z=1.; printf(" %5.3lf",z); Z[n][k]=z;}
    5 KB (785 words) - 14:24, 20 June 2013
  • Tetration
    : \({\rm tet}_b(z\!+\!1) = \exp_b\!\big( {\rm tet}_b(z) \big)\) ...ast for \(b\!>\!1\), is holomorphic at least in \(\{ z \in \mathbb C : \Re(z)\!>\!-2\}\).
    21 KB (3,175 words) - 23:37, 2 May 2021
  • Tetre2215.cc
    // Plot of tetrational \(f={\rm tet}_b(z)\)<br> z_type FIT1(z_type d,z_type z){
    6 KB (1,030 words) - 18:48, 30 July 2019
  • Conto.cin
    #define z(m,n) Z[(m)*N1+(n)] #define zmn z(m,n)
    13 KB (2,858 words) - 06:59, 1 December 2018
  • Fukushima disaster, timeline of links
    Wang N., Wu X., Kehrwald N., Li Z., Li Q., Jiang X., Pu J. Fukushima nuclear accident recorded in tibetan pla
    146 KB (19,835 words) - 18:25, 30 July 2019
  • 4t1c.cc
    main(){ int j,k,m,n; DB x,y,z, p,q, t;
    3 KB (564 words) - 18:33, 28 April 2023
  • Mapping
    ...8-09-02188-7/home.html D.Kouznetsov. (2009). Solutions of \(F(z+1)=\exp(F(z))\) in the complex plane.. Mathematics of Computation, 78: 1647-1670. DOI:1 ...cae, v.81, p.65-76 (2011)</ref> is holomorphic solution \(F(z)={\rm tet}_b(z)\) of the equations
    14 KB (2,275 words) - 18:25, 30 July 2019
  • Катынь-2
    <ref name="call"> http://thomas.loc.gov/cgi-bin/query/z?c111%3AH.RES.1489%3A Mr.KING. Bill Text 111th Congress (2009-2010) H.RES.14 ...a brzoza nie miała wpływu na pierwotne zniszczenie skrzydła - to jedna z kluczowych konkluzji raportu technicznego podkomisji smoleńskiej.
    145 KB (3,277 words) - 00:40, 25 March 2022
  • Katyn-2
    <ref name="call"> http://thomas.loc.gov/cgi-bin/query/z?c111%3AH.RES.1489%3A Mr.KING. Bill Text 111th Congress (2009-2010) H.RES.14 Opracowanie to będzie służyć jako jeden z etapów na drodze do utworzenie tak bardzo potrzebnej międzynarodowej komi
    107 KB (7,830 words) - 15:02, 4 January 2022
  • Superfunction
    \(\displaystyle {{F(z)} \atop \,} {= \atop \,} {T^z(t) \atop \,} {= \atop \,}
    25 KB (3,622 words) - 08:35, 3 May 2021
  • Natural pentation
    \(\mathrm{pen}(z\!+\!1)=\mathrm{tet}\Big(\mathrm{pen}(z) \Big)\) \(\displaystyle \mathrm{pen}(z)= \sum_{m=0}^{M-1} \alpha_m \mathrm e^{mkz} + O(\mathrm e^{Mkz})\)
    7 KB (1,090 words) - 18:49, 30 July 2019
  • Place of science in the human knowledge
    D.Kouznetsov. Analytic solution of F(z+1)=exp(F(z)) in complex z-plane. Mathematics of Computation, v.78 (2009), 1647-1670.
    100 KB (14,715 words) - 16:21, 31 October 2021
  • Место науки в человеческом знании
    http://link.springer.com/article/10.1007/s00424-006-0169-z?LI=true#page-1 Marco Piccolino. Luigi Galvani and animal electricity: two c ...ERS/2010superfar.pdf D.Kouznetsov. Solution of F(z+1)=exp(F(z)) in complex z-plane. [[Mathematics of Computation]], <b>78</b>, No.267, p.1647-1670 (2009
    111 KB (2,581 words) - 16:54, 17 June 2020
  • Logiu.cin
    // \(T(z)=4 z (1\!-\!z)\) z_type J(z_type z){ return .5-sqrt(.25-z/Q); }
    3 KB (513 words) - 18:48, 30 July 2019
  • Square root of factorial
    ...[[Factorial]]), or \(\sqrt{!\,}\) is solution \(h\) of equation \(h(h(z))=z!\). ...l}\). It is assumed that \(z\!=\!2\) is [[regular point]] of \(\sqrt{!\,}(z)\), and
    13 KB (1,766 words) - 18:43, 30 July 2019
  • Arcfactorial
    : \( \mathrm{Factorial}(\mathrm{ArcFactorial}(z))=z\) However, \(\mathrm{Factorial}^{-1}(z)\) should not be confused with
    3 KB (414 words) - 18:26, 30 July 2019
  • Holomorphic extension of the Collatz subsequence
    : \(h(F(z))=F(z\!+\!1)\) : \(h(F(z))-F(z\!+\!1)=0\)
    5 KB (798 words) - 18:25, 30 July 2019
  • Regular Iteration
    :$\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\! (1) ~ ~ ~ F(z\!+\!1)=T(F(z))$ :$\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\! (2) ~ ~ ~ \displaystyle F(z) = L+\sum_{n=1}^{N} a_n \varepsilon^n + o(\varepsilon^N)$ , where $\varepsi
    20 KB (3,010 words) - 18:11, 11 June 2022
  • SuperFactorial
    : \(\mathrm{SuperFactorial}(z)=\mathrm{Factorial}^z(3)\) : \(\mathrm{Factorial}(\mathrm{SuperFactorial}(z))=\mathrm{SuperFactorial}(z\!+\!1)\)
    18 KB (2,278 words) - 00:03, 29 February 2024
  • Transfer equation
    : \(F(z\!+\!1)=h(F(z))\) for all \(z\in C \subseteq \mathbb C\).
    3 KB (519 words) - 18:27, 30 July 2019
  • Abel function
    : \(G(T(z))=G(z)+1\) In certain range of values of \(z\), this equation is equivalent of the [[Transfer equation]]
    4 KB (547 words) - 23:16, 24 August 2020
  • Transfer function
    D.Kouznetsov. Analytic solution of F(z+1)=exp(F(z)) in complex z-plane. Mathematics of Computation, v.78 (2009), 1647-1670. : \((1) ~ ~ ~ ~ ~ F(z\!+\!1)=h(F(z))\)
    11 KB (1,644 words) - 06:33, 20 July 2020
  • Abel equation
    : \((1)~ ~ ~ ~ ~ G(T(z))=G(z)+1\) at least for \(z\) from some domain in the complex plane.
    4 KB (598 words) - 18:26, 30 July 2019
  • Navier-Stokes equation
    ...}{r} \frac{\partial u_r}{\partial \phi} + u_z \frac{\partial u_r}{\partial z} - \frac{u_{\phi}^2}{r}\right) = ...^2}\frac{\partial^2 u_r}{\partial \phi^2} + \frac{\partial^2 u_r}{\partial z^2}-\frac{u_r}{r^2}-\frac{2}{r^2}\frac{\partial u_\phi}{\partial \phi} \righ
    7 KB (1,149 words) - 18:26, 30 July 2019
  • Logarithm
    :\( \exp(\ln(z))=z ~ ~\) for all from the range of definition; : \(\exp_b(z)=b^z\)
    4 KB (661 words) - 10:12, 20 July 2020
  • Nest
    :\(\mathrm{Nest}[f,z,c]\) where \(f\) is name of iterated function, \(z\) is initial value of the argument, and \(c\) is number of iterations.
    3 KB (438 words) - 18:25, 30 July 2019
  • Japan
    | doi= 10.1007/s00340-005-2083-z | doi= 10.1007/s00340-005-2083-z
    15 KB (2,106 words) - 13:37, 5 December 2020
  • Microchip atom trap
    ...plied Physics B 82 (3): 363–366.(2006). <!-- doi:10.1007/s00340-005-2083-z !--> ...agnet traps, [[Ioffe configuration trap]]s, [[QUIC trap]]s and others. The z-type trap shown in the picture happened to be to easy to manufacture and ef
    9 KB (1,400 words) - 18:26, 30 July 2019
  • Quantum reflection
    ...has translational symmetry in two directions (say <math>y</math> and <math>z</math>), such that only a single coordinate (say <math>x</math>) is importa
    16 KB (2,453 words) - 18:26, 30 July 2019
  • ArcTetration
    D.Kouznetsov. Analytic solution of F(z+1)=exp(F(z)) in complex z-plane. Mathematics of Computation 78 (2009), 1647-1670. : \( \mathrm{ate}_b(\mathrm{tet}_b(z))=z \)
    7 KB (1,091 words) - 23:03, 30 November 2019
  • Fixed point
    ...cally analytic function with hyperbolic fixpoint at \(0\), i.e. \(f(z)=c_1 z + c_2z^2 + \dots\), \(|c_1|\neq 0,1\), there is always a locally analytic a <math>\sigma(f(z))=c_1 \sigma(z))\</math>
    4 KB (574 words) - 18:26, 30 July 2019
  • B271az.cc
    main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d, cu,cd; DO(n,N1){y=Y[n]; z=z_type(x,y);
    3 KB (529 words) - 14:32, 20 June 2013
  • Fslog.cin
    // To call this function at complex argument z, type '''FSLOG(z)''' z_type z=z1-1.; z/=2.;
    5 KB (275 words) - 07:00, 1 December 2018
  • Class of equivalence
    ...(\mathbb Z\) is used to denote the set of integer numbers; \(m \in \mathbb Z\). \( \mathbb N \subset \mathbb Z\)
    7 KB (1,216 words) - 18:25, 30 July 2019
  • Holomorphic function
    ...C\), there is defined function \(f(z) \in \mathbb C\) such that for any \(z \in C\) there exist the derivative ...ystyle f'(z)= \lim_{t \rightarrow 0,~ t\in \mathbb C}~ \frac{f(z\!+\!t)-f(z)}{t}
    1 KB (151 words) - 21:08, 25 January 2021
  • Tania function
    f'(z)= \frac{f(z)}{1+f(z)} ...nd then along the straight line (parallel to the real axis) to the point \(z\).
    27 KB (4,071 words) - 18:29, 16 July 2020
  • LambertW function
    ...nction." From MathWorld--A Wolfram Web Resource. </ref>, is solution \(W=W(z)\) of equations ...tyle \!\!\!\!\!\!\!\!\!\!\!\!\!\!\! (0\mathrm{a}) ~ ~ ~ W'= \frac{W}{(1+W)~z}\)
    8 KB (1,107 words) - 18:26, 30 July 2019
  • Doya function
    In vicinity of the real axis (While \(|\Im(z)| \!<\! \pi\)), the [[Doya function]] can be expressed through the \mathrm{Doya}(z)=\mathrm{LambertW}\Big( z~ \mathrm{e}^{z+1} \Big)\)
    19 KB (2,778 words) - 10:05, 1 May 2021
  • Doya.cin
    z_type ArcTania(z_type z) {return z + log(z) - 1. ;} z_type ArcTaniap(z_type z) {return 1. + 1./z ;}
    3 KB (480 words) - 14:33, 20 June 2013
  • Table of superfunctions
    : \( \!\!\!\!\!\!\!\!\!\!\!\! (1) ~ ~ ~ F(z+1)=T(F(z)) \) : \( \!\!\!\!\!\!\!\!\!\!\!\! (2) ~ ~ ~ G(T(z))=G(z)+1 \)
    11 KB (1,565 words) - 18:26, 30 July 2019
  • Square root of exponential
    : \(\!\!\!\!\!\!\!\!\!\!\!\!\!(1) ~ ~ ~ \varphi(\varphi(z))=z\) ...) is assumed to be [[holomorphic function]] for some domain of values of \(z\).
    5 KB (750 words) - 18:25, 30 July 2019
  • Quantum Mechanics
    ...ot \</math>1/\sin(z)<math>); and \</math>\exp^2(z)\\]means <math>\exp(\exp(z))\</math>, but not \\[\exp(z)^2\\]and not <math>\exp(z^2)\</math>.</ref>.
    7 KB (1,006 words) - 18:26, 30 July 2019
  • Iteration
    [[File:PowIteT.jpg|400px|thumb|Fig.1. Iterates of \(T(z)=z^2~\): \(~y\!=\!T^n(x)\!=\!x^{2^n}~\) for various \(n\)]] [[File:ExpIte4T.jpg|360px|thumb|Fig.3. Iterates of \(T(z)=\exp(z)~\): \(~y\!=\!T^n(x)\!=\!\exp^n(x)~\) ]]
    14 KB (2,203 words) - 06:36, 20 July 2020
  • Theorem
    D.Kouznetsov. Analytic solution of F(z+1)=exp(F(z)) in complex z-plane. Mathematics of Computation, v.78 (2009), 1647-1670.
    2 KB (248 words) - 14:33, 20 June 2013
  • Natural tetration
    : \(\exp(\mathrm{tet}(z))= \mathrm{tet}(z\!+\!1)\) ...on of the [[Transfer equation]] \( \mathrm{tet}(z\!+\!1)=\exp(\mathrm{tet}(z)) \).
    14 KB (1,972 words) - 02:22, 27 June 2020
  • Квадратный корень из факториала
    : \(f(f(z))=z!\) ...7/home.html D.Kouznetsov. Analytic solution of F(z+1)=exp(F(z)) in complex z-plane. Mathematics of Computation, v.78 (2009), 1647-1670.
    6 KB (312 words) - 18:33, 30 July 2019
  • Iterated integral
    D^{-1} \mathrm {e}^{px}=\int_0^x \mathrm{e}^{pz} \mathrm d z ...\(u\) an \(v\) representable in form (6), and \(g(z)=\alpha u(z) + \beta v(z)\)
    9 KB (1,321 words) - 18:26, 30 July 2019
  • Корень из факториала
    : \(h(h(z))=z\) для некоторого домена значений \(z\).
    7 KB (381 words) - 18:38, 30 July 2019
  • Уравнение Шредера
    : \( \!\!\!(1) ~ ~ ~ T(f(z))=f(kz)\) : \(\!\!\!(2) ~ ~ ~ T(F(z))=F(z+1)\)
    5 KB (116 words) - 18:37, 30 July 2019
  • Коррупция
    Евгения Альбац. Кто вы, доктор Z? № 5 (274) от 18 февраля 2013 года.</ref>. Он состои ...ч активистов за компьютерами». Блогер doct-z — о создании глобального проекта по поис
    219 KB (3,034 words) - 19:23, 7 November 2021
  • Filog.cin
    ...\(\exp(z)\) is evaluated with routine complex double Filog(complex double z) below z_type ArcTania(z_type z) {return z + log(z) - 1. ;}
    2 KB (258 words) - 10:19, 20 July 2020
  • Filog
    \(f=\mathrm{Filog}(z)\) is solution of the equation for base \(b\!=\!\exp(z)\).
    4 KB (572 words) - 20:10, 11 August 2020
  • Tetration to Sheldon base
    ...\!\!\! (1) \displaystyle ~ ~ ~ \exp(a~ \mathrm{tet_s}(z)) = \mathrm{tet}_s(z\!+\!1)\) ...ex half-line, except some facility of the negative part of the real axis \(z<-2\); the tetration should have the cutline there.
    5 KB (707 words) - 21:33, 13 July 2020
  • GLxw2048.inc
    ...-5718-09-02188-7/home.html D.Kouznetsov. (2009). Solutions of F(z+1)=exp(F(z)) in the complex plane.. Mathematics of Computation, 78: 1647-1670.</ref>. { int m,j,i; long double z1,z,xm,xl,pp,p3,p2,p1;
    108 KB (1,626 words) - 18:46, 30 July 2019
  • Iterated Cauchi
    T(F(z))=F(z+1) It is assumed that \(F(z)\) is holomorphic at least in the strip \(\Re(z)\le 1\), and
    6 KB (987 words) - 10:20, 20 July 2020
  • Institute for Laser Science
    | doi=10.1007/s00340-005-2083-z http://maps.google.com/maps?q=34.85,138.55&ie=UTF8&om=1&z=19&ll=35.657952,139.54128&spn=0.001077,0.002942&t=h
    12 KB (1,757 words) - 07:01, 1 December 2018
  • Fsexp.cin
    // complex<double>FSEXP( complex <double> z) z_type fima(z_type z){ z_type c,e;
    9 KB (654 words) - 07:00, 1 December 2018
  • Факториал
    : \( F(z)=z\cdot F(z\!-\!1)\) : \(\mathrm{Factorial}(z)=z!\)
    2 KB (59 words) - 18:33, 30 July 2019
  • ArcCos
    : \( \cos(\arccos(z))=z\) ...phic in the whole complex plane except the halflines \(z\!\le\! -1\) and \(z\!\ge\! 1\).
    5 KB (754 words) - 18:47, 30 July 2019
  • ArcCip
    : \(\displaystyle \mathrm {Cip}(z)=\frac{\cos(z)}{z}\) <!-- Complex map of function Cip is shown at right.!--> : \(\displaystyle \mathrm{Cip}(\mathrm{ArcCip}(z))=z\).
    8 KB (1,211 words) - 18:25, 30 July 2019
  • SuperFactorial.cin
    z_type superfac0(z_type z){ int n; z_type s; z_type e=exp(k*z);
    1 KB (88 words) - 14:55, 20 June 2013
  • Fac.cin
    z_type fracti(z_type z){ z_type s; int n; DB a[17]= s=a[16]/(z+19./(z+25./(z))); for(n=15;n>=0;n--) s=a[n]/(z+s);
    4 KB (487 words) - 07:00, 1 December 2018
  • ArcSin
    : \(\displaystyle \sin(z) = \frac{\exp(\mathrm i z)- \exp(-\mathrm i z)}{2~ \mathrm i}\) \(f=\arcsin(z)\) is holomorphic solution \(f\) of equation
    9 KB (982 words) - 18:48, 30 July 2019
  • Coshc
    : \(\displaystyle \mathrm{coshc}(z)=\frac{\cosh(z)}{z}\) : \(\displaystyle \cosh(z)=\cos(\mathrm i z) = \frac{\mathrm e^z+\mathrm e^{-z} }{2}\)
    4 KB (509 words) - 18:26, 30 July 2019
  • ArcCosc
    : \( \displaystyle \mathrm{cosc}(z)=\frac{\cos(z)}{z}\) : \(\displaystyle \mathrm{sinc}(z)=\frac{\sin(z)}{z}\)
    8 KB (1,137 words) - 18:27, 30 July 2019
  • Cosc
    : \( \displaystyle \mathrm{cosc}(z)=\frac{\cos(z)}{z}\) : \( \displaystyle \mathrm{sinc}(z) = \frac{ \sin(z)}{z}\)
    4 KB (649 words) - 18:26, 30 July 2019
  • Wakame
    : \(\!\!\!\!\!\!\!\!\! (4) ~ ~ ~ ~ \mathrm{cohc}(z)=\frac{\cosh(z)}{z}\); ...\!\!\!\! (5) ~ ~ ~ ~ \mathrm{cohc}'(z)=\frac{\sinh(z)}{z}-\frac{\cosh(z)}{z^2}\)
    4 KB (581 words) - 18:25, 30 July 2019
  • Sazae-san constants
    ...{\cosh(z)}{z} ~,~\) \(~ ~ \displaystyle \mathrm{cosc}(z) = \frac{\cos(z)}{z}\) ...{\sinh(z)}{z} ~,~ \) \(~ ~ \displaystyle \mathrm{sinc}(z) = \frac{\sin(z)}{z} \)
    4 KB (495 words) - 18:47, 30 July 2019
  • Acosq
    : \(\mathrm{acosq}(z)=\mathrm{acosc}\left( \mathrm e ^{\mathrm i \pi/4} \,z \right)\) main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
    4 KB (656 words) - 18:25, 30 July 2019
  • Acosc.cin
    // ArcCosc is [[inverse function]] of [[Cosc]]; \(\text{cosc}(z) = \cos(z)/z\). z_type cosc(z_type z) {return cos(z)/z;}
    1 KB (219 words) - 18:46, 30 July 2019
  • ArcCosqq
    : \(\text{acosqq}(z)=\text{acosq}(z)\, \tan\!\!\big( \text{acosq}(z) \big)\) : \(\text{acosq}(z)=\text{acosq}\big( \mathrm e ^{\mathrm i \pi /4}\, z \big)\)
    2 KB (216 words) - 18:26, 30 July 2019
  • Acosc1.cin
    z_type acos(z_type z){ if(Im(z)<0){if(Re(z)>=0){return I*log( z + sqrt(z*z-1.) );}
    3 KB (436 words) - 18:47, 30 July 2019
  • Acosc1
    \(f=\mathrm{Acosc1}(z)\) is solution of equation : \( \displaystyle \mathrm{cosc}(f)=z\)
    6 KB (896 words) - 18:26, 30 July 2019
  • ArcFactorial
    : \( \mathrm{Factorial}(\mathrm{ArcFactorial}(z))=z\) However, \(\mathrm{Factorial}^{-1}(z)\) should not be confused with
    3 KB (376 words) - 18:26, 30 July 2019
  • Paraxial approximation
    ...\!\!\!\!\!\ (2) ~ ~ ~ \Psi=\Psi( \vec x, z)=\exp(\mathrm i k z)\psi(\vec x,z)\) ...(2) into (1) and neglecting term with second derivative with respect to \(z\) gives
    3 KB (496 words) - 18:25, 30 July 2019
  • Absorbing Schroedinger
    ...al case, the particle propagates mainly along some coordinate, let it be \(z\), and the potential depends only on the transversal coordinates. ...\!\!\!\!\!\!\!\!\!\! (6) ~ ~ ~ \psi=\mathrm e ^{\mathrm i (c+\mathrm i s) z }\)
    15 KB (2,070 words) - 18:47, 30 July 2019
  • BesselJ0
    J_0''(z)+ J_0'(z)/z+
    6 KB (913 words) - 18:25, 30 July 2019
  • ArcSinc
    ...nc}(z)= \frac{\sin(z)}{z}~\), \(~~\mathrm{sinc}\big(\mathrm{asinc}(z)\big)=z\) : \( \displaystyle \mathrm{acosc}(z^*)= \mathrm{acosc}(z)^*\)
    4 KB (563 words) - 18:27, 30 July 2019
  • Guiding of waves between absorbing walls
    ...is assumed, and it is supposed that mainly the particle propagates along \(z\) axis, and \(x\) is called the transversal coordinate.!--> ...psi= \psi(x,z)\) and \(\nabla\) differentiates with respect to \(x\) and \(z\).
    5 KB (743 words) - 18:47, 30 July 2019
  • BesselK0
    f''(z)+f(z)/z=f(z) K_0(z) = \exp(-z)\sqrt{\frac{\pi}{2z}} ~ \Big( 1+ O(1/z)\Big)
    3 KB (394 words) - 18:26, 30 July 2019
  • BesselY0
    solution \(f=f(z)\) of the Bessel equation f''+f'/z+f=0\)
    3 KB (445 words) - 18:26, 30 July 2019
  • Cylindric function
    : \(\!\!\!\!\!\!\!\!\!\!\! (1) ~ ~ ~ z^2 f''(z) + z f'(z) + (z^2-\nu^2) f(z)=0\) : \(\!\!\!\!\!\!\!\!\!\!\! (2) ~ ~ ~ H_\nu(z)=J_\nu(z)+\mathrm i Y_\nu(z)\)
    3 KB (388 words) - 18:26, 30 July 2019
  • BesselJ1
    : \(\!\!\!\! \mathrm{BesselJ1}(z)=J_1(z)= \mathrm{BesselJ}[1,z]\) f''(z)+f'(z)/z + (z^2\!-\!1)f(z) = 0\)
    3 KB (439 words) - 18:26, 30 July 2019
  • Besselj0.cin
    z_type BesselJ0o(z_type z){ int n; z_type c,s,t; s=1.; c=1.; t=-z*z/4.; for(n=1;n<32;n++) {c/=0.+n*n; c*=t; s+=c;}
    2 KB (190 words) - 18:47, 30 July 2019
  • Besselj1.cin
    // BesselJ[1,z] implementation: z_type BesselJ1o(z_type z){ int n; z_type c,s,t;
    2 KB (159 words) - 14:59, 20 June 2013
  • Bessel function
    \( \!\!\!\!\!\!\!\!\! (1) ~ ~ ~ f''(z)+f'(z)/z+(1-\nu/z^2)f(x) =0\) Due to singularity of the equation at \(z=0\), the regular solution should have specific behavior. This solution is c
    13 KB (1,592 words) - 18:25, 30 July 2019
  • Bessely0.cin
    ...elj0.cin]] is also required for the evaluation of BesselY0(\(z\)) at \(\Re(z) < 0\). z_type BesselY0o(z_type z){ z_type q=z*z, L=log(z),c;
    4 KB (370 words) - 18:46, 30 July 2019
  • BesselH0
    [[BesselH0]]\((z)=H_0(z)\!=\)[[HankelH1]]\([0,z]\) is the [[Cylindric function]] H (called also the [[Hankel function]]) o : \(H_0(z)=J_0(z)+\mathrm i Y_0(z)\)
    4 KB (509 words) - 18:26, 30 July 2019
  • Ocean wave solution
    The only two spatial coordinates \(Z\) and \(Y\) are used; and the letter \(Z\) is not necessary for the third spatial coordinate. There fore it is used ...!\!\!\!\!\!\!(2) ~ ~ ~ ~ Z=\mathrm{Serega}(z)=z+\mathrm i ~ \exp(\mathrm i z^*)\)
    12 KB (1,879 words) - 18:26, 30 July 2019
  • Serega.cin
    z_type Serega(z_type z){ DB x,y, p,q, r,s,c; int n; x=Re(z); y=Im(z); z_type ArcSerega(z_type z){ DB x,y ,X,Y,X0,Y0, r,s,c, rc,rs, dX, dY; int n;
    1 KB (265 words) - 15:00, 20 June 2013
  • Serega function
    ...on''' is nongolomorphic function \(\mathrm{Serega}\) of complex variable \(z\) such that : \(F(z)=x+\mathrm i ~ \exp(\mathrm i ~ z^*)\)
    5 KB (674 words) - 18:25, 30 July 2019
  • LogisticSequence
    ...\!\!\!\!\!\!\!\!(1) ~ ~ ~ ~ \mathrm{LogisticOperator}_s(z) = s\,z \,(1\!-\!z)\) where \(z\) is complex number and \(s\) is real number; usually it is assumed that \(
    7 KB (886 words) - 18:26, 30 July 2019
  • Efjh.cin
    z_type J(z_type z){ return .5-sqrt(.25-z/Q); } z_type H(z_type z){ return Q*z*(1.-z); }
    3 KB (364 words) - 07:00, 1 December 2018
  • ArcLogisticSequence
    ...\!\!\!\!\!\! (1) ~ ~ ~ T(z)=\mathrm{LogisticOperator}_s(z)= s\, z\, (1\!-\!z)\) ...~ ~ \mathrm{ArcLogisticSequence}_s(T(z))= \mathrm{ArcLogisticSequence}_s(z)+1\)
    3 KB (380 words) - 18:25, 30 July 2019
  • Logistic operator
    ...\!\!\!\!\!\!\!\!(1) ~ ~ ~ ~ \mathrm{LogisticOperator}_s(z) = s\,z \,(1\!-\!z)\) : \(\!\!\!\!\!\!\!\!\!\!\!(2) ~ ~ ~ ~ F(z\!+\!1)=T(F(z))\)
    6 KB (817 words) - 19:54, 5 August 2020
  • WrightOmega
    f'(z)= \frac{f(z)}{1+f(z)} ...nd then along the straight line (parallel to the real axis) to the point \(z\).
    4 KB (610 words) - 10:22, 20 July 2020
  • Keller function
    ...ler Institute of Quantum Electronics HPT E 16.3 Auguste-Piccard-Hof 1 8093 Zürich ...\!\!\!\! (1) ~ ~ ~ \mathrm{Keller}(z)=z+ \ln\!\Big(\mathrm e - \mathrm e^{-z}(\mathrm e-1) \Big)\)
    10 KB (1,479 words) - 05:27, 16 December 2019
  • Shoko function
    :\( \!\!\!\!\!\!\!\!\!\! (1) ~ ~ ~ \mathrm {Shoko}(z)=\ln\Big(1+\mathrm e^z (\mathrm e -1) \Big)\) ...!\!\!\!\!\!\!\!\!\! (2) ~ ~ ~ \mathrm {Shoko}(z)= (\mathrm e -1) \mathrm e^z+ O(\mathrm e^{2z})\)
    10 KB (1,507 words) - 18:25, 30 July 2019
  • Shoka function
    :\( \mathrm{Shoka}(z)=z+\ln\!\Big( \exp(-z) +\mathrm e -1\Big)\) ...=\mathrm{Shoka}^{-1}\) can be expressed as elementary function; for \(|\Im(z)| < \pi\),
    3 KB (421 words) - 10:23, 20 July 2020
  • ArcShoka
    : \( \displaystyle \mathrm{ArcShoka}(z)= z + \ln\!\left( \frac{\mathrm e^z-1}{\mathrm e-1} \right)\) :\( T(F(z))=F(z\!+\!1)\)
    3 KB (441 words) - 18:26, 30 July 2019
  • ArcKeller
    ...\!\!\!\! (1) ~ ~ ~ \mathrm{Keller}(z)=z+ \ln\!\Big(\mathrm e - \mathrm e^{-z}(\mathrm e-1) \Big)\) ...left( \frac{1}{\mathrm e}+\frac{\mathrm e \!-\!1}{\mathrm e}\, \mathrm e^{-z} \right)\)
    4 KB (545 words) - 18:26, 30 July 2019
  • Superfactorial.cin
    z_type superfac0(z_type z){ int n; z_type s; z_type e=exp(k*z);
    1 KB (88 words) - 15:01, 20 June 2013
  • Facp.cin
    z_type infp0(z_type z) s=c[29]; for(n=28;n>=0;n--){ s*=z; s+=c[n];} return s;}
    3 KB (353 words) - 15:01, 20 June 2013
  • Afacc.cin
    z_type afacb(z_type z){ z_type t=(log(z)-F0)/c2; z_type v=sqrt(t);
    995 bytes (148 words) - 18:46, 3 September 2023
  • Abelfac.cin
    z_type arcsuperfac0(z_type z){ int n; z_type s, c, e; // z-=2.; s=U[15]*z; for(n=14;n>=0;n--){ s+=U[n]; s*=z;}
    1 KB (124 words) - 15:01, 20 June 2013
  • F45E.cin
    z_type f45E(z_type z){int n; z_type e,s; e=exp(.32663425997828098238*(z-1.11520724513161));
    1 KB (139 words) - 18:48, 30 July 2019
  • F45L.cin
    z_type f45L(z_type z){ int n; z_type e,s; z-=4.;
    2 KB (163 words) - 18:47, 30 July 2019
  • ArcLambertW
    (1) \(~ ~ ~ \mathrm{ArcLambertW}(z) = \mathrm{zex}(z) = z \exp(z) \) In wide ranges of values of \(z\), the relations
    3 KB (499 words) - 18:25, 30 July 2019
  • SuZex
    ...on]] of [[ArcLambertW]], denoted also as [[zex]], \(\mathrm{zex}(z)=z \exp(z)\). ...\!\!\!\!(2) ~ ~ ~ \mathrm{SuZex}(z\!+\!1)=\mathrm{zex}\Big(\mathrm{SuZex}(z)\Big)\)
    7 KB (1,076 words) - 18:25, 30 July 2019
  • Путаница
    ..., и тогда, например, выражения \(f(0)\) или \(f(z)\) имеют не больше смысла, чем запись \(\displa
    8 KB (210 words) - 18:33, 30 July 2019
  • Tania.cin
    z_type ArcTania(z_type z) {return z + log(z) - 1. ;} z_type ArcTaniap(z_type z) {return 1. + 1./z ;}
    1 KB (209 words) - 15:01, 20 June 2013
  • SuZex approximation
    ...of function [[SuZex]], which is [[superfunction]] of [[zex]]\(\,(z)=z\exp(z)~\). The [[complex map]] of [[SuZex]] is shown in figure at right. Below, i (1) \(~ ~ ~ T(z)=\mathrm{zex}(z) = z\,\exp(z)~\)
    14 KB (2,037 words) - 18:25, 30 July 2019
  • SuZexCoef20.cin
    ...x_1)=a[0][0]/z + (a[1][0]+a[1][1]L)/z^2 + (a[2][0]+a[2][1] L + a[2][2]L^2)/z^3 + .. // and L=Log[z] or L=Log[-z]
    6 KB (180 words) - 15:01, 20 June 2013
  • SuZex.cin
    ...is [[superfunction]] for the [[transfer function]] T(z)=[[zex]](z)= z exp(z) <br> z_type zex(z_type z) { return z*exp(z);}
    12 KB (682 words) - 07:06, 1 December 2018
  • LambertW.cin
    z_type LambertWo(z_type z){ int n,m=48; z_type d=-z; return z*(1.+s); }
    5 KB (287 words) - 15:01, 20 June 2013
  • AuZex.cin
    // z_type zex(z_type z) { return z*exp(z) ; } z_type AuZexAsy(z_type z){ int m=15,n; z_type s;
    3 KB (274 words) - 15:01, 20 June 2013
  • AuZex
    ...o [[Abel function]] for the [[transfer function]] \(\mathrm{zex}(z)=z \exp(z)\). ...]] is [[Inverse function]] of [[SuZex]], so, in wide ranges of values of \(z\), the relations
    6 KB (899 words) - 18:44, 30 July 2019
  • Power function
    (1) \(~ ~ ~ \mathrm{pow}_a(z) = z^a = \exp_z(a) = \exp(a \ln(z))\) ...is assumed that \(a\) is real. The real-real plot of function \(T(z)\!=\!z^a\) is shown in Fig.1 for several values of \(a\).
    15 KB (2,495 words) - 18:43, 30 July 2019
  • Trappmann function
    \(~\mathrm{Tra}(z)=\mathrm e^z +z~\) ...hrm{ArcTra}(z)=\) \(z-\mathrm{Tania}(z\!-\!1)=\) \( z-\mathrm{WrightOmega}(z)\)
    9 KB (1,320 words) - 11:38, 20 July 2020
  • Уравнение Шредера для растворимости
    \( \!\!\!(1) ~ ~ ~ T(f(z))=f(kz)\)<br>
    3 KB (47 words) - 18:36, 30 July 2019
  • Schroeder equation
    (1) \(~ ~ ~ g\Big(T(z)\Big)= s \, g(z)\) ...se \(~s~\) from both sides of equation (1), assuming that \(~s~\) and \(~g(z)~\) are not real negative number nor zero. This gives
    8 KB (1,239 words) - 11:32, 20 July 2020
  • Fractional iterate
    (1) \(~ ~ ~ t_r^m(z)=T^n(z)~\) for all \(~z~\) in some vicinity of \(~L~\).
    2 KB (272 words) - 18:25, 30 July 2019
  • Zooming equation
    (1) \(~ ~ ~ T\big(f(z)\big)= f( K\, z)~\) (2) \(~ ~ ~ g\big(T(z)\big)= K \, g(z) \)
    10 KB (1,627 words) - 18:26, 30 July 2019
  • Regular iterate
    ...is supposed to be [[fractional iterate]] of function \(T\), id est, for \(z\) in vicinity of point \(L\), (1) \( ~ ~ ~ f^n(z)=T^m(z)\)
    1 KB (178 words) - 06:42, 20 July 2020
  • SuTra
    </ref> of the [[Trappmann function]], \(~\mathrm{tra}(z)=z+\exp(z)~\). ...behaves as \(z\rightarrow -\ln(-z)\) at large \(z\) for the most of \(\arg(z)\), id set, in the whole complex plane except the strip along the real axis
    9 KB (1,285 words) - 18:25, 30 July 2019
  • SuFac.cin
    z_type superfac0(z_type z){ int n; z_type s; z_type e=exp(k*z);
    2 KB (119 words) - 07:06, 1 December 2018
  • AuFac.cin
    ...values of z, \(\rm AuFac(Sufac(z))\!=\!z~\) and \(~\rm SuFac(Aufac(z))\!=\!z~\). z_type arcsuperfac0(z_type z){ int n; z_type s, c, e;
    2 KB (137 words) - 18:46, 30 July 2019
  • ArcTra
    (1)\(~ ~ ~ \mathrm{tra}(z)=z+\exp(z)\) (2) \(~ ~ ~ \mathrm{ArcTra}(z)=z-\mathrm{Tania}(z-1)\)
    10 KB (1,442 words) - 18:47, 30 July 2019
  • AuTra
    ...[[Abel function]] of the [[Trappmann function]], \(\mathrm{tra}(z)=z+\exp(z)\). \( \mathrm{AuTra} \Big( \mathrm{tra}(z) \Big)= \mathrm{AuTra}(z)+1\)
    6 KB (1,009 words) - 18:48, 30 July 2019
  • AuTra.cin
    z_type arctra(z_type z){return z-Tania(z-1.);} z_type tra(z_type z) {return z+exp(z);}
    1 KB (197 words) - 15:03, 20 June 2013
  • F4ten.cin
    z _type f4ten(z_type z){ //NOT SHIFTED FOR x1 !!!! ...){t=Aten*GLx[k]; c+= GLw[k]*( G[k]/(z_type( 1.,t)-z) - E[k]/(z_type(-1.,t)-z) );}
    2 KB (287 words) - 15:03, 20 June 2013
  • Fit1.cin
    ...=\exp(a)\) for \(0.05<a<2\) ; \(\mathrm{tet}_b(z)\) is approximated for \(|z|<1\) using the fruncated Taylor expansion of // \(\mathrm{tet}_b(z) - \ln(z+2)\)
    3 KB (402 words) - 18:48, 30 July 2019
  • Logistic
    T(z)=q\cdot z \cdot (1-z) <math> F(z\!+\!1)=T(F(z))
    3 KB (411 words) - 18:26, 30 July 2019
  • Цыбко Константин Валерьевич
    http://vk.com/club32160205?z=photo-32160205_304217834%2Fwall-32160205_6475 http://vk.com/club32160205?z=photo-32160205_304216982%2Fwall-32160205_6470
    15 KB (187 words) - 07:36, 1 December 2018
  • Sunflower as adsorbent of cesium
    Soudek P, Valenová S, Vavríková Z, Vanek T.
    6 KB (856 words) - 07:06, 1 December 2018
  • File:Factorialz.jpg
    In the complex <math>z</math>-plane, the lines of constant <math>u=\Re(z!)</math> and
    (1,219 × 927 (479 KB)) - 08:35, 1 December 2018
  • File:FactoReal.jpg
    z_type expauno(z_type z) {int n,m; DB x,y; z_type s; s=expaunoc[24]; x=Re(z);if(x<-.9) return expauno(z+1.)-log(z+1.);
    (915 × 1,310 (141 KB)) - 08:35, 1 December 2018
  • File:OneOverFactorial.jpg
    Complex map of f(z)=1/z! in the complex z plane. Copy from
    (1,244 × 949 (276 KB)) - 17:50, 20 June 2013
  • File:AbelFacMapT.png
    $\mathrm{AbalFactorial}(z)=\mathrm{Factorial}^z(3)$ main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
    (1,412 × 1,395 (372 KB)) - 17:17, 25 September 2013
  • File:AbelFacPloT.png
    z_type arcsuperfac0(z_type z){ int n; z_type s, c, e; // z-=2.; s=U[15]*z; for(n=14;n>=0;n--){ s+=U[n]; s*=z;}
    (1,673 × 1,308 (136 KB)) - 09:43, 21 June 2013
  • File:AbelFactorialMap.png
    int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(x,y);
    (675 × 673 (120 KB)) - 08:28, 1 December 2018
  • File:AbelFactorialR.png
    :$G(z!)=G(z)+1$
    (1,060 × 705 (34 KB)) - 09:39, 21 June 2013
  • File:AciplotTa.png
    z_type Cip(z_type z) {return cos(z)/z;} z_type Cipp(z_type z) {return (-sin(z) - cos(z)/z)/z ;}
    (1,267 × 1,267 (84 KB)) - 09:41, 21 June 2013
  • File:AcipmapTjpg.jpg
    z_type Cip(z_type z) {return cos(z)/z;} z_type Cipp(z_type z) {return (-sin(z) - cos(z)/z)/z ;}
    (1,759 × 1,746 (661 KB)) - 09:41, 21 June 2013
  • File:AcipmapTpng.png
    z_type Cip(z_type z) {return cos(z)/z;} z_type Cipp(z_type z) {return (-sin(z) - cos(z)/z)/z ;}
    (844 × 838 (199 KB)) - 09:41, 21 June 2013
  • File:AcomapT200.png
    z_type acos(z_type z){ if(Im(z)<0){if(Re(z)>=0){return I*log( z + sqrt(z*z-1.) );}
    (2,345 × 2,328 (1.06 MB)) - 09:41, 21 June 2013
  • File:Acosc1mapT.png
    main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(x,y);
    (1,759 × 1,746 (862 KB)) - 09:41, 21 June 2013
  • File:Acosc1plotT.png
    main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; /* M(Tarao,Sazae) DO(m,200){x=-.33+.01*(m+.5); z=x; DB t=x-Tarao0, u=sqrt(t);
    (851 × 2,728 (203 KB)) - 09:41, 21 June 2013
  • File:AcoscmapT300.png
    z_type cosc(z_type z) {return cos(z)/z;} z_type cosp(z_type z) {return (-sin(z) - cos(z)/z)/z ;}
    (3,517 × 3,492 (1.64 MB)) - 09:41, 21 June 2013
  • File:AcoscplotT.png
    : $\displaystyle \mathrm{Left}_3(z)=\mathrm{Sazae} \frac{2(z-\mathrm{Tarao})}
    (1,267 × 1,267 (152 KB)) - 09:41, 21 June 2013
  • File:AcosmapT200.png
    z_type acos(z_type z){ if(Im(z)<0){if(Re(z)>=0){return I*log( z + sqrt(z*z-1.) );}
    (1,773 × 1,752 (797 KB)) - 09:41, 21 June 2013
  • File:AcosplotT.png
    z_type acos(z_type z){ if(Im(z)<0){if(Re(z)>=0){return I*log( z + sqrt(z*z-1.) );}
    (897 × 1,387 (69 KB)) - 09:41, 21 June 2013
  • File:Acosq1plotT.png
    $\mathrm{acosq}_1(z)=\mathrm{acosc}_1\left( \mathrm e ^{ \mathrm i \pi/4 } z \right)$ :\mathrm{expan}_1(z)=\frac{3 \pi}{2}
    (2,512 × 3,504 (379 KB)) - 09:41, 21 June 2013
  • File:AcosqplotT100.png
    :$ \mathrm{acosq}(z)=\mathrm{acosc}\left( \mathrm e^{\mathrm i \pi/4}\, z\right)$ for real values of $z$.
    (2,231 × 1,215 (152 KB)) - 09:41, 21 June 2013
  • File:AcosqqplotT.png
    : $\text{acosqq}(z)=\text{acosq}(z)\, \tan\!\!\big( \text{acosq}(z) \big)$ : $\text{acosq}(z)=\text{acosq}\big( \mathrm e ^{\mathrm i \pi /4}\, z \big)$
    (1,686 × 1,823 (148 KB)) - 09:41, 21 June 2013
  • File:AfacmapT800.png
    z_type fracti(z_type z){ z_type s; int n; DB a[17]= s=a[16]/(z+19./(z+25./(z))); for(n=15;n>=0;n--) s=a[n]/(z+s);
    (2,355 × 2,334 (1.03 MB)) - 09:41, 21 June 2013
  • File:AfacplotT2px300.png
    main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
    (2,534 × 1,267 (141 KB)) - 09:41, 21 June 2013
  • File:ArcCipMapT.jpg
    z_type Cip(z_type z) {return cos(z)/z;} z_type Cipp(z_type z) {return (-sin(z) - cos(z)/z)/z ;}
    (1,759 × 1,746 (661 KB)) - 09:41, 21 June 2013
  • File:ArcKellerMapT.png
    ...left( \frac{1}{\mathrm e}+\frac{\mathrm e \!-\!1}{\mathrm e}\, \mathrm e^{-z} \right)$ // z_type Shoko(z_type z) { return log(1.+exp(z)*(M_E-1.)); }
    (1,773 × 1,752 (924 KB)) - 08:29, 1 December 2018
  • File:ArcSeregaMapT.png
    : $ \mathrm {Serega}(z)=z+\mathrm i \exp( \mathrm i ~ z^*)$ // z_type Serega(z_type z);
    (1,312 × 1,312 (483 KB)) - 09:43, 21 June 2013
  • File:ArcShokaMapT.png
    z_type Shoko(z_type z){ return log(1.+exp(z)*(M_E-1.)); } z_type Shoka(z_type z) { return z + log(exp(-z)+(M_E-1.)); }
    (1,773 × 1,752 (1,010 KB)) - 08:29, 1 December 2018
  • File:ArcTaniaMap.png
    :$ \mathrm{ArcTania}(z)= z+\ln(z) -1$ z_type ArcTania(z_type z) {return z + log(z) - 1. ;}
    (851 × 841 (626 KB)) - 08:30, 1 December 2018
  • File:ArcTraMapT.jpg
    //z_type zex(z_type z){ return z*exp(z);} //z_type tra(z_type z){ return z+exp(z);}
    (2,576 × 2,559 (1.31 MB)) - 08:30, 1 December 2018
  • File:AsimapT.png
    z_type acos(z_type z){ if(Im(z)<0){if(Re(z)>=0){return I*log( z + sqrt(z*z-1.) );}
    (1,759 × 1,746 (746 KB)) - 09:41, 21 June 2013
  • File:AsincmapT.png
    z_type acos(z_type z){ if(Im(z)<0){if(Re(z)>=0){return I*log( z + sqrt(z*z-1.) );}
    (1,759 × 1,746 (896 KB)) - 09:41, 21 June 2013
  • File:AsincplotT500.png
    z_type acos(z_type z){ if(Im(z)<0){if(Re(z)>=0){return I*log( z + sqrt(z*z-1.) );}
    (843 × 2,014 (184 KB)) - 09:41, 21 June 2013
  • File:AsinplotT.png
    z_type acos(z_type z){ if(Im(z)<0){if(Re(z)>=0){return I*log( z + sqrt(z*z-1.) );}
    (897 × 1,381 (70 KB)) - 09:41, 21 June 2013
  • File:AuTraMapT.jpg
    ...l function]] of the [[Trappmann function]] $\mathrm{tra}(z)\!=\!z\!+\!\exp(z)$. z_type arctra(z_type z){return z-Tania(z-1.);}
    (4,367 × 4,317 (1.82 MB)) - 08:30, 1 December 2018
  • File:AuTraPlotT.jpg
    $ \mathrm{tra}(z)=z+\exp(z)$ z_type tra(z_type z){ return exp(z)+z;}
    (1,678 × 1,262 (172 KB)) - 08:30, 1 December 2018
  • File:AuZexLamPlotT.jpg
    main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; FILE *o;o=fopen("AuZexLam.eps","w"); ado(o,1204,404);
    (2,508 × 841 (169 KB)) - 08:30, 1 December 2018
  • File:AuZexMapT.jpg
    // z_type zex(z_type z) { return z*exp(z) ; } z_type LambertWo(z_type z){ int n,m=48; z_type d=-z;
    (4,367 × 4,326 (1.53 MB)) - 08:30, 1 December 2018
  • File:B271a.png
    D.Kouznetsov. Analytic solution of F(z+1)=exp(F(z)) in complex z-plane. Mathematics of Computation, v.78 (2009), 1647-1670. <!-- :$ \mathrm{ate}(\exp(z))=\mathrm{ate}(z)\!+\!1~,$
    (1,609 × 1,417 (506 KB)) - 08:30, 1 December 2018
  • File:B271t.png
    main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d, cu,cd; DO(n,N1){y=Y[n]; z=z_type(x,y); if(abs(z+2.)>.04)
    (1,609 × 1,417 (791 KB)) - 08:30, 1 December 2018
  • File:B271t3T.png
    main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d, cu,cd; DO(n,N1){y=Y[n]; z=z_type(x,y); //if(abs(z+2.)>.019)
    (1,742 × 1,726 (1,007 KB)) - 08:30, 1 December 2018
  • File:BesselH0mapT050.png
    main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(x,y);
    (1,420 × 721 (966 KB)) - 09:42, 21 June 2013
  • File:Besselh0mapT100.png
    : $H_0(z)=J_0(z)+\mathrm i Y_0(z)$ main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
    (2,284 × 1,164 (1.65 MB)) - 08:31, 1 December 2018
  • File:Besselj0j1plotT.png
    main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
    (3,405 × 484 (112 KB)) - 09:42, 21 June 2013
  • File:Besselj0map1T080.png
    z_type BesselJ0o(z_type z){ int n; z_type c,s,t; s=1.; c=1.; t=-z*z/4.; for(n=1;n<32;n++) {c/=0.+n*n; c*=t; s+=c;}
    (1,827 × 932 (1.7 MB)) - 09:41, 21 June 2013
  • File:Besselj0mapT100.png
    z_type BesselJ0o(z_type z){ int n; z_type c,s,t; s=1.; c=1.; t=-z*z/4.; for(n=1;n<32;n++) {c/=0.+n*n; c*=t; s+=c;}
    (1,173 × 1,164 (1.45 MB)) - 09:41, 21 June 2013
  • File:Besselj1mapT080.png
    // BesselJ[1,z] implementation: z_type BesselJ1o(z_type z){ int n; z_type c,s,t;
    (2,056 × 1,048 (1.72 MB)) - 09:42, 21 June 2013
  • File:Besselk0mapT900.png
    z_type besselk0o(z_type z){ z_type L=log(z); z_type t=z*z; z_type besselk0O(z_type z){ z_type t=1./z, q=sqrt(t); z_type s;
    (2,118 × 2,105 (1.62 MB)) - 09:41, 21 June 2013
  • File:BesselY0J0J1plotT060.png
    main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
    (1,362 × 217 (47 KB)) - 09:42, 21 June 2013
  • File:BesselY0mapWideT039.png
    ...tion]] of zero order, id est, the [[BesselY0]]; $Y_0(z)=\mathrm{BesselY}[0,z]$ the expansion at small values of $|z|$ and the expansion for the large values. (See the implementation at [[Bess
    (2,191 × 563 (1.91 MB)) - 09:42, 21 June 2013
  • File:CihplotT.png
    main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; //z=x; y=Re(ACip5(z));
    (1,267 × 1,059 (87 KB)) - 09:41, 21 June 2013
  • File:CipmapT.jpg
    [[Complex map]] of function $\mathrm{Cip}(z)=\cos(z)/z$. main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
    (1,759 × 1,746 (1.58 MB)) - 08:32, 1 December 2018
  • File:CipmapT.png
    [[Complex map]] of function $\mathrm{Cip}(z)=\cos(z)/z$. main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
    (844 × 838 (484 KB)) - 09:41, 21 June 2013
  • File:CoscmapT100.png
    main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(x,y);
    (2,284 × 1,164 (1.75 MB)) - 09:41, 21 June 2013
  • File:CoshcmapT120.png
    z_type acos(z_type z){ if(Im(z)<0){if(Re(z)>=0){return I*log( z + sqrt(z*z-1.) );}
    (1,407 × 1,397 (1.47 MB)) - 09:41, 21 June 2013
  • File:CoshcplotT.png
    : $\displaystyle \mathrm{coshc}(z)=\frac{\cosh(z)}{z}$ : $\cosh(z)=(\mathrm e^z+\mathrm e^{-z})/2$
    (465 × 851 (36 KB)) - 09:41, 21 June 2013
  • File:Doya10map4bT60.png
    main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(x,y);
    (714 × 700 (342 KB)) - 08:34, 1 December 2018
  • File:Doya20map4bT100.png
    main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(x,y);
    (1,190 × 1,167 (663 KB)) - 08:34, 1 December 2018
  • File:Doya500.png
    main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(y,x);
    (153 × 237 (55 KB)) - 00:19, 14 July 2020
  • File:DoyaconT70.png
    z_type ArcTania(z_type z) {return z + log(z) - 1. ;} z_type ArcTaniap(z_type z) {return 1. + 1./z ;}
    (442 × 817 (98 KB)) - 09:39, 21 June 2013
  • File:Doyam10map4bT100.png
    main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(x,y);
    (1,199 × 1,167 (629 KB)) - 09:39, 21 June 2013
  • File:DoyaPlotT100.png
    $ \mathrm{Doya}_t(z)=\mathrm{Tania}(t+\mathrm{ArcTania}(z))$ $\displaystyle \mathrm{Tania}'(z)=
    (580 × 590 (77 KB)) - 08:34, 1 December 2018
  • File:DoyaplotTc.png
    main(){ int j,k,m,n; DB x,y,t,e, a; z_type z; M(0,0); for(n=1;n<151;n++){x=.02*n;z=x;y=Re(Doya(1.,z)); L(x,y)}
    (881 × 1,325 (95 KB)) - 09:43, 21 June 2013
  • File:E1efig09abc1a150.png
    main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d, cu,cd; DO(n,N1){y=Y[n]; z=z_type(x,y);
    (2,234 × 711 (883 KB)) - 08:34, 1 December 2018
  • File:Elutin1a4tori.jpg
    F[c_, z_] = 1/2 (1 - Cos[2^c ArcCos[1 - 2 z]]) : $f^c(z)=F(c+G(z))$
    (922 × 914 (62 KB)) - 09:38, 21 June 2013
  • File:Esqrt2iterMapT.png
    $T(x) = \Big(\sqrt{2}\Big){^z}= \exp_b(z)$ $T^{1/3}(z)=F\!\left(\frac{1}{3}+G(z)\right)$
    (1,092 × 1,080 (1.36 MB)) - 09:43, 21 June 2013
  • File:Expc.jpg
    <math>\exp^c(z)=\mathrm{tet}\Big(c+\mathrm{tet}^{-1}(z)\Big)</math>
    (941 × 852 (48 KB)) - 18:39, 11 July 2013
  • File:ExpIte4T.jpg
    // z_type tra(z_type z){ return exp(z)+z;} // z_type F(z_type z){ return log(suzex(z));}
    (1,673 × 1,673 (901 KB)) - 08:35, 1 December 2018
  • File:ExpMapT.png
    main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d, cu,cd; DO(n,N1){y=Y[n]; z=z_type(x,y); //if(abs(z+2.)>.019)
    (1,742 × 1,726 (1.62 MB)) - 08:35, 1 December 2018
  • File:ExpQ2mapT.png
    main(){ int j,k,m,n; DB x,y, p,q, t,r; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(x,y);
    (1,765 × 1,729 (1.15 MB)) - 08:35, 1 December 2018
  • File:FacIteT.jpg
    //DB F(DB z) { return exp( exp( log(B)*z));} //DB G(DB z) { return log( log(z) )/log(B);}
    (2,093 × 2,093 (795 KB)) - 08:35, 1 December 2018
  • File:FacmapT500.png
    z_type fracti(z_type z){ z_type s; int n; DB a[17]= s=a[16]/(z+19./(z+25./(z))); for(n=15;n>=0;n--) s=a[n]/(z+s);
    (2,355 × 2,334 (1.73 MB)) - 09:41, 21 June 2013
  • File:Filogbigmap100.png
    ...og}(z)$ expresses the [[fixed point]] of [[logarithm]] to base $b\!=\!\exp(z)$. $\mathrm{Filog}(z^*)^*$
    (2,870 × 2,851 (847 KB)) - 08:36, 1 December 2018
  • File:Filogmap300.png
    ...og}(z)$ expresses the [[fixed point]] of [[logarithm]] to base $b\!=\!\exp(z)$. $\mathrm{Filog}(z^*)^*$
    (893 × 897 (292 KB)) - 09:40, 21 June 2013
  • File:FilogmT1000a.jpg
    \( z=\mathrm{Filog}(a)~\) expresses solution \(z\) of equation \(\ln(z)/a=z\). int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
    (4,359 × 2,989 (1.68 MB)) - 03:45, 21 July 2020
  • File:Hades500.png
    main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(y,x);
    (153 × 237 (55 KB)) - 09:39, 21 June 2013
  • File:IterEq2plotU.png
    DB F(DB z) { return exp( exp( log(B)*z));} DB G(DB z) { return log( log(z) )/log(B);}
    (2,944 × 2,944 (986 KB)) - 21:42, 27 September 2013
  • File:IterPowPlotT.png
    ...c function, id est, [[power function]] for power 2; $y=\mathrm{Pow}_2^{~c}(z)=T^c(x)~$ for various values of number $c$ of iteration. Here, : $\!\!\!\!\!\!\!\!\!\!\ (1) ~ ~ ~ T(z)=\mathrm{Pow}_2(z)=z^2=\exp\Big(\ln(z)\,2\Big)$
    (2,093 × 2,093 (680 KB)) - 20:50, 28 September 2013
  • File:KellerDoyaT.png
    z_type Shoka(z_type z) { return z + log(exp(-z)+(M_E-1.)); } z_type ArcShoka(z_type z){ return z + log((1.-exp(-z))/(M_E-1.)) ;}
    (661 × 881 (70 KB)) - 08:39, 1 December 2018
  • File:KellerMapT.png
    $\mathrm{Keller}(z)=z+\ln\!\Big(\mathrm e-(\mathrm e\!-\!1) \mathrm e^{-z}\Big)$. z_type Shoka(z_type z) { return z + log(exp(-z)+(M_E-1.)); }
    (1,773 × 1,752 (1 MB)) - 08:39, 1 December 2018
  • File:KellerPlotT.png
    z_type Shoka(z_type z) { return z + log(exp(-z)+(M_E-1.)); } z_type ArcShoka(z_type z){ return z + log((1.-exp(-z))/(M_E-1.)) ;}
    (870 × 885 (118 KB)) - 08:39, 1 December 2018
  • File:LambertWmap150.png
    z_type ArcTania(z_type z) {return z + log(z) - 1. ;} z_type ArcTaniap(z_type z) {return 1. + 1./z ;}
    (1,773 × 1,752 (523 KB)) - 08:41, 1 December 2018
  • File:LambertWplotT.png
    #define Re(z) z.real() #define Im(z) z.imag()
    (1,267 × 839 (81 KB)) - 09:43, 21 June 2013
  • File:Logi1a345T300.png
    $ \mathrm{LogisticPoerator}_s^{\,c}(z)= \mathrm{LogisticSequence}_s\Big( c + \mathrm{ArcLogisticSequence}(z) \big)$
    (1,636 × 565 (184 KB)) - 08:41, 1 December 2018
  • File:Logi2c3T1000.png
    z_type J(z_type z){ return .5-sqrt(.25-z/Q); } z_type H(z_type z){ return Q*z*(1.-z); }
    (1,772 × 1,758 (1.36 MB)) - 08:41, 1 December 2018
  • File:Logi2c4T1000.png
    z_type J(z_type z){ return .5-sqrt(.25-z/Q); } z_type H(z_type z){ return Q*z*(1.-z); }
    (1,772 × 1,758 (1.39 MB)) - 08:41, 1 December 2018
  • File:Logi2d3T1500.png
    main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(x,y);
    (2,657 × 2,657 (1.47 MB)) - 08:41, 1 December 2018
  • File:Logi5T1500.png
    int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
    (3,404 × 540 (185 KB)) - 06:28, 10 June 2022
  • File:Logi5U1500.png
    main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
    (3,404 × 955 (403 KB)) - 06:30, 10 June 2022
  • File:LogiarcT300.png
    main(){ int j,k,m,n; DB x0,y0,x,y, p,q, t; z_type z,c,d; DO(m,1250) { x=x0-.001*m; z=E(x); y=Re(z); L(x,y); if( y<-2.01) break; }
    (598 × 1,287 (90 KB)) - 09:43, 21 June 2013
  • File:LogQ2mapT2.png
    main(){ int j,k,m,n; DB x,y, p,q, t,r; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(x,y);
    (1,765 × 1,729 (1.43 MB)) - 09:43, 21 June 2013
  • File:MicroChipAtomicTrap00.jpg
    ...ield is realized at the side of the chip, close to the central part of the z-electrode with electric current. The movement of atoms along the wire is limited by the angles of the "Z". Additional electrodes were designed to play with the effective potential
    (890 × 976 (44 KB)) - 09:39, 21 June 2013
  • File:Modeab02T.png
    z_type acosq(z_type z){ z_type c=z*exp(I*M_PI/4.); c=acosc(c); return c;} z_type acosqq(z_type z){ z_type c=z*exp(I*M_PI/4.); c=acosc(c); return c*tan(c);}
    (1,678 × 519 (66 KB)) - 09:41, 21 June 2013
  • File:Modeab25T.png
    z_type acosq(z_type z){ z_type c=z*exp(I*M_PI/4.); c=acosc(c); return c;} z_type acosqq(z_type z){ z_type c=z*exp(I*M_PI/4.); c=acosc(c); return c*tan(c);}
    (1,678 × 519 (76 KB)) - 09:41, 21 June 2013
  • File:Modeabso25T.png
    z_type acosq(z_type z){ z_type c=z*exp(I*M_PI/4.); c=acosc(c); return c;} z_type acosqq(z_type z){ z_type c=z*exp(I*M_PI/4.); c=acosc(c); return c*tan(c);}
    (2,657 × 905 (262 KB)) - 09:41, 21 June 2013
  • File:ObamaPutin.jpg
    ...kolí? No ano, hlavně USA. Jak nejefektivněji dosáhnou USA toho, že se z Ruska stane slabá země? Správně, dosadí na nejvyšší post svého age
    (488 × 634 (111 KB)) - 08:45, 1 December 2018
  • File:PowIteT.jpg
    ...c function, id est, [[power function]] for power 2; $y=\mathrm{Pow}_2^{~c}(z)=T^c(x)~$ for various values of number $c$ of iteration. Here, : $\!\!\!\!\!\!\!\!\!\!\ (1) ~ ~ ~ T(z)=\mathrm{Pow}_2(z)=z^2=\exp\Big(\ln(z)\,2\Big)$
    (2,093 × 2,093 (1.01 MB)) - 08:46, 1 December 2018
  • File:PowPloT.jpg
    //DB F(DB z) { return exp( exp( log(B)*z));} //DB G(DB z) { return log( log(z) )/log(B);}
    (2,097 × 2,097 (697 KB)) - 09:44, 21 June 2013
  • File:QFacMapT.png
    $f(z)=\mathrm{Factorial}^{1/2}(z)$ $f(z)= \mathrm{SuperFactorial}\Big(0.5+\mathrm{AbelFactorial}(z)\Big)$
    (1,412 × 1,395 (1.47 MB)) - 09:43, 21 June 2013
  • File:QFactorialQexp.jpg
    : <math> H\big(S(z)\big)=S(z\!+\!1)</math> : <math> H^c(z)=S(c+S^{-1}(z))</math>
    (800 × 399 (121 KB)) - 17:23, 11 July 2013
  • File:SazaeconT.png
    ...=\frac{\cos(z)}{z} ~,$ $~ ~ \displaystyle \mathrm{cohc}(z)=\frac{\cosh(z)}{z} ~,$ main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
    (2,118 × 1,682 (216 KB)) - 09:41, 21 June 2013
  • File:SeregaFunction03.png
    main(){ int n; DB x,y,t,c,s,z; FILE *o; DO(n,1260){t=-3.04+.005*n; c=cos(t); s=sin(t); z=1.3-c; z*=z;
    (2,509 × 434 (51 KB)) - 08:51, 1 December 2018
  • File:Sfaczoo300.png
    main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(x,y);
    (1,142 × 453 (302 KB)) - 00:12, 29 February 2024
  • File:ShokaMapT.png
    ...]] of the [[Shoka function]], $\mathrm{Shoka}(z)=z-\ln\!\Big( \mathrm e^{-z} +\mathrm e -1 \Big)$ : ...that of the [[Shoko function]], $\mathrm{Shoko}(z)=\ln\!\Big(1+ \mathrm e^z (\mathrm e \!-\! 1) \Big)$
    (1,773 × 1,752 (992 KB)) - 08:51, 1 December 2018
  • File:ShokoMapT.png
    z_type Shoko(z_type z) { return log(1.+exp(z)*(M_E-1.)); } main(){ int j,k,m,n; DB x,y, p,q, t,r; z_type z,c,d;
    (1,773 × 1,752 (964 KB)) - 09:43, 21 June 2013
  • File:SimudoyaTb.png
    :$T(z)=\mathrm{Doya}_1(z)=\mathrm{LambertW}\Big( z~ \mathrm{e}^{z+1} \Big)$ main(){ int j,k,m,n; DB x,y,t,e, a; z_type z;
    (3,388 × 1,744 (537 KB)) - 08:51, 1 December 2018
  • File:SincmapT100.png
    main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(x,y);
    (2,284 × 1,164 (1.63 MB)) - 09:41, 21 June 2013
  • File:SincplotT.png
    main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
    (3,350 × 1,001 (221 KB)) - 09:41, 21 June 2013
  • File:SqrtExpZ.jpg
    [[Complex map]]s of function <math>f=\exp^c(z)</math> in the <math>z</math> plane D.Kouznetsov. Analytic solution of F(z+1)=exp(F(z)) in complex z-plane. Mathematics of Computation, v.78 (2009), 1647-1670.
    (842 × 953 (83 KB)) - 11:56, 21 June 2013
  • File:Sqrt2figf45bT.png
    :$ \displaystyle \tilde f(z)= \sum_{n=0}^{N-1} a_n \exp(knz)$ $T(z)=\exp_{\sqrt{2}}(z)=\Big( \sqrt{2} \Big)^z$
    (2,180 × 2,159 (1.01 MB)) - 08:52, 1 December 2018
  • File:Sqrt2figf45eT.png
    z_type f45E(z_type z){int n; z_type e,s; e=exp(.32663425997828098238*(z-1.11520724513161));
    (2,180 × 2,159 (1.18 MB)) - 08:52, 1 December 2018
  • File:Sqrt2figL45eT.png
    z_type f45E(z_type z){int n; z_type e,s; e=exp(.32663425997828098238*(z-1.11520724513161));
    (2,180 × 2,159 (1.07 MB)) - 12:53, 20 July 2020
  • File:SuperFacMapT.png
    main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; DO(n,N1){y=Y[n]; z=z_type(x,y);
    (1,412 × 1,395 (457 KB)) - 09:43, 21 June 2013
  • File:SuperFacPlotT.png
    : $\mathrm{Factorial}(z\!+\!1)=(z\!+\!1)\, \mathrm{Factorial}(z)~$, $~\mathrm{Factorial}(0)\!=\!1$ [[SuperFactorial]]$(z)=\mathrm{Factorial}^z(3)$ is holomorphic solution of equations
    (1,673 × 2,109 (181 KB)) - 09:43, 21 June 2013

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